As a general guide a Eurail pass is only value on days where you will travel a reasonable distance.

Longer duration passes are cheaper per day but that only applies if you use them on more days.

For days spent within a city and suburbs Eurail is not a good option, there are nearly always cheaper local tickets and crucially Eurail is only valid on the railway lines, not the metros, trams and buses that will be more useful for getting around cities.

Germany will have a ticket available costing €49 for 1 month valid on all city, local and regional transport. The German cities you listed are all within a region and connectable using the regional trains with that ticket, only Frankfurt - Cologne would be substantially cheaper using IC/ICE trains that a Eurail Pass would be useful for.

It would be a good idea to get an idea of where you plan on travelling, this map gives an overview of main rail routes https://www.interrail.eu/content/dam/pdfs/Interrail%20map%202022.pdf

You can then use a good journey planner such as https://www.bahn.com/en to see what services/times are like. You can then get a better idea what combination of tickets will best match your plans.

It is far too early to see timetables for Dec 2023 so look up times for this month and you will get a good idea of the general schedules, times do not change that much from month to month. The only thing you should be aware of is the Christmas and new year period where there can be significant changes to the regular timetables.

I would point out that  a fixed pass for 15 days in 2 months will cost 518/627 euros (2nd/1st) whereas a continuous 2 month pass will only cost an extra 250/320 euro for an extra 25 days of unlimited rail travel. In many countries this would facilitate high speed/IC day trips or regional connections to local tourist attractions. In Germany for example you could easily do day trips from Koblenz along the Rhine or to the Black Forest with stays up to 8 hours. An ICE train easily covers 100 Km (60 miles) an hour so a 9am start gives lunch in Freiburg, an afternoon touring and back for dinner. Even Belgium or Bavaria are reachable)

In addition it means you do not have to force long distance journeys just to save travel days - e.g. if you went to Sicily from Rome it is a 10 to 12 hour journey just about doable in one travel day, but with an unlimited pass you could split it into a 2 travel day  journey and enjoy a later start with a stop in Naples or Salerno (for Pompeii).

Although there are many local schemes in most of Europe and buying individual tickets can save a few euros on the daily pass cost, I am willing to bet the eventual saving over 25 days against the additional cost of a continuous pass will be insignificant. The savings will be overwhelmed by the loss of flexibility and sheer hassle of trying to balance which of the 15 days pass  you will use against paying as you go.

You cannot argue that local transport is not included because that is the same whichever pass you decide on. 

Many of the pre-purchased (cheaper) tickets are for specific trains and non-refundable or exchangeable and on the day prices can be very high in some countries, whereas with a pass you simply get on the next available (with only an extra reservation cost if needed).